Question

if x+2y=7 and 2x+y=8 are the diameters of a circle with radius 4 units ,find the equation of the circle

Answer 1

Answer:

(x - 2)² + (y - 2)² = 16

Step-by-step explanation:

An equation of a circle is (x - a)² + (y - b)² = r² , where (a, b) are coordinates of a center and "r" is a radius of a center of a circle.

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Because given linear equations are the diameters of a circle, then the solution of the system of equations

$\left \{ {{x+2y=7} \atop {2x+y=8}} \right.$

is a center of a circle.

y = 8 - 2x

x + 2(8 - 2x) = 7 ⇒ x = 3

y = 8 - 2(3) ⇒ y = 2

Point (3, 2) is a center of the circle with radius 4.

(x - 2)² + (y - 2)² = 16